AnswersFL-1200700-Mathematics for College Algebra MISSolving One-Variable Inequalities

Solving One-Variable Inequalities — Unit test Answers

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1
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What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?

A
–12 – 20x ≤ –6x + 9
B
–12 – 20x ≥ –6x + 9
C
–12 + 20x ≤ –6x + 9
D
–12 + 20x ≥ –6x + 9
2
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What value of x is in the solution set of 2x – 3 > 11 – 5x?

A
–3
B
0
C
2
D
4
3

Step 1: –10 + 8x < 6x – 4Step 2: –10 < –2x – 4Step 3: –6 < –2xStep 4: ________

A
x < –3
B
x > –3
C
x < 3
D
x > 3
4

Solve the inequality.2(4x – 3) ≥ –3(3x) + 5x?

A
x ≥ 0.5
B
x ≥ 2
C
(–∞, 0.5]
D
(–∞, 2]
5

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
6

Which answer choice results from using the distributive property to rewrite the expression below?5(x + 8)

A
5x + 40
B
5x + 8
C
5(8x)
D
5 + 8x
7

Arianna correctly simplified an expression. When she substituted into the simplified expression, the value was –4. Which could be Arianna’s original expression?

Question illustration
A
One-sixth (negative 3 x minus 24)
Option A
B
One-sixth (negative 5 x minus 8)
Option B
C
One-sixth (negative 10 x minus 4)
Option C
D
One-sixth (negative 12 x minus 16)
Option D
8

Elaina simplified the algebraic expression below. Hannah claimed that Elaina did not finish the process. Which answer shows the simplified expression that Hannah expected?

Question illustration
A
2 y squared minus 7 y + 6
Option A
B
2 y squared + 7 y + 6
Option B
C
4 y squared minus 7 y + 6
Option C
D
4 y squared + 7 y + 6
Option D
9

Which procedure justifies whether is equivalent to ?

Question illustration
A
The expressions are not equivalent because and .
Option A
B
The expressions are not equivalent because and .
Option B
C
The expressions are equivalent because and .
Option C
D
The expressions are equivalent because and .
Option D
10

What is the simplified expression for the expression below? 4(x + 8) + 5(x – 3)

A
9x + 5
B
9x + 11
C
9x + 17
D
9x + 47
11

What is the simplified expression for ?

Question illustration
A
Negative a squared + 5 a b + 8
Option A
B
Negative a squared minus 13 a b + 5 + 3
Option B
C
a squared + 5 a b + 8
Option C
D
a squared minus 13 a b + 5 + 3
Option D
12

Step 1: Subtract 3 from both sides of the inequality.Step 2: __________Step 3: Divide both sides of the inequality by the coefficient of x.

A
Add 2x to both sides of the inequality.
B
Subtract 8x from both sides of the inequality.
C
Subtract 2x from both sides of the inequality.
D
Add 8x to both sides of the inequality.
13

Mickey simplified the expression below. He then checked his work by substituting 4 for x. He noticed his two values were not equal. What was Mickey’s error when simplifying?ExpressionSimplified Expression

Question illustration
A
Mickey should have added –4 and 2 when combining the coefficients of the x terms.
B
Mickey should have added 2 and 1 when combining the terms.
Option B
C
Mickey should have added 9 and 3 when combining the constant terms.
D
Mickey should have added –4 and –1 when combining the x terms.
14

What value of x is in the solution set of 3(x – 4) ≥ 5x + 2?

A
–10
B
–5
C
5
D
10
15

Which number line represents the solution set for the inequality –x ≥ 4?

Question illustration
A
A number line from negative 10 to 10 in increments of 2. A point is at negative 2 and a bold line starts at negative 2 and is pointing to the left.
Option A
B
A number line from negative 10 to 10 in increments of 2. A point is at negative 8 and a bold line starts at negative 8 and is pointing to the left.
Option B
C
A number line from negative 10 to 10 in increments of 2. A point is at negative 2 and a bold line starts at negative 2 and is pointing to the right.
Option C
D
A number line from negative 10 to 10 in increments of 2. A point is at negative 8 and a bold line starts at negative 8 and is pointing to the right.
Option D
16

Tomas’s math class held a raffle. The student who picked the ticket with a pair of equivalent equations on it would win. Which is the winning ticket?

A
x squared minus 3 x y + 4 minus 2 x squared = negative x squared minus 2 x y minus x y + 4
Option A
B
.
Option B
C
3 a squared minus a b + 3 minus 3 a b = 6 a squared minus 2 a b + 3 minus 2 a b
Option C
D
9 s squared minus s t + 5 minus 3 s t = 6 s squared minus 3 s t + 5 + 3 s squared
Option D
17

Tao wants to check that the expression 3(4x – 6) simplifies to 12x – 18. What is the value when 2 is substituted for x into both expressions?

A
The value of each expression is 2.
B
The value of each expression is 6.
C
The value of one expression is 2, and the value of the other expression is 6.
D
The value of one expression is 6, and the value of the other expression is –6.
18

Which is the first step in simplifying the expression 2(x + 3) + 5?

A
2x + 2(3) + 5
B
2x + 3 + 5
C
2 + x + 3 + 5
D
2(5) + x + 3
19

Which is a correct first step in solving 5 – 2x < 8x – 3?

A
5 < 6x – 3
B
3x < 8x – 3
C
5 < 10x – 3
D
2 – 2x < 8x
20

Jose combined the like terms in the expression. Marc claims that he made a mistake. Jose asks Marc to explain how to fix his error. Which is the best explanation that Marc can give Jose?

Question illustration
A
Jose, you should have added 12 and –12 for the xy terms.
B
Jose, you should have added –8 and –5 for the for the terms.
Option B
C
Jose, you should have added –17 and 1 for the terms.
Option C
D
Jose, you should have added –8 and the two 12s for the xy terms.

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